Table REF  gives results. The point estimate for \(\tau \)  suggests that overall, vaccinated units were more protected than placebo ones, by a difference of 2.4 additional cases prevented/fewer cases caused per thousand for the vaccinated units. The point estimate for \(\delta \)  suggests the difference between vaccine and placebo was larger in the less vaccinated group, with the difference in the differences estimated to be 2.2 cases per thousand. These are substantial differences when compared to the observed cholera rates, and are equivalent to point estimates for \(\tau _1\)  and \(\tau _2\)  of -3.5 and -1.3 cases per thousand. The estimates are consistent with the values of \(DE(\alpha )\)  reported in [1]}, in that the estimates for \(\tau _1\)  and \(\tau _2\)  equal \(DE(\alpha )\)  for values of \(\alpha \)  that belong to their respective vaccination categories.
